Gauge Parameter Dependence of the 1-loop Fermion Self Energy at Finite Temperature

We show a gauge parameter dependence of the 1-loop fermion self energy at finite temperature before the analytic continuation. We also show a gauge parameter dependence of only the temperature dependence term. The result is the same as the ladder approximation Schwinger-Dyson equation. The wave function renormalization constant approaches 1 by taking a negative gauge parameter. The analogy of the ladder approximation Schwinger-Dyson equation and the 1-loop calculation will help the analysis of the phase transition.